ludwig457
Find the area of an equilateral triangle with side of length 18. (Round your answer to one decimal place.)



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ludwig457
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Area= 1/2 base x height
tan(60)=h/18
h=18tan(60)
right?

ludwig457
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should i be using law of sines

lgbasallote
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why use law of sines?

lgbasallote
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wait...by law of sines do you mean \[\frac{a}{\sin A} = \frac b{\sin B} = \frac c{\sin C}\]

ludwig457
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yes, i have three angles (60) and three sides)
so the how would i then find the height

lgbasallote
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use pythagorean theorem...you have equilateral triangle dw:1352707222314:dw

lgbasallote
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so the height would cut your triangle into two equal parts..dw:1352707262694:dw can you see how to get the height now?

ludwig457
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15.6?

lgbasallote
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yes

lgbasallote
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now use your 1/2 bh

ludwig457
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A=(1/2)(18)15.6)

lgbasallote
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yes

lgbasallote
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by the way.. you can also use your solution a while ago... 18tan (60) you don't need law of sines...just use a calculator for that

ludwig457
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140.4units squared

lgbasallote
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yes

ludwig457
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and that solution from earlier would then give me the height?

lgbasallote
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hmm wait...something's wrong with it...let me find it first

ludwig457
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should it be 9 instead of 18

lgbasallote
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yes it should be 9